Yay, this is one of my favourite topics:)
I didn't read all the posts (yet), because I am so excited that there is a topic about immortality, I have to post my idea!
Since I know about death and actually understood the concept of life I wanted to find a way of not dying (I guess everyone thinks about it at least once in his/her life) and I found an alternative way of immortality. First of all I don't believe in god or in the existence of any other higher being, so I wanted a solution using pure science. Let's assume that physics is quite good enough to describe our world, the universe. The main concept in my immortality theory is that everything is built of smaller objects. The exact details are irrelevant, does not matter how the larger objects are built or what are they called or anything like that. Let's assume that the world is infinite large and the time is infinite as well. This means that there was something before the big bang and there will be something after an infinite long time as well. Now let's describe a person as a series of objects, in this case the objects will be the smallest objects in the universe. If there is no smallest object, i.e. everything is built of an even smaller object and this is true for every object (this is some kind of recursion) then take the smallest object that actually has an effect on a scale which can be detected by us. Assuming that the world is infinite large and the time is infinite as well the probability that there is an exact same series of object as me is not zero.
This means that if I wait for an infinite long time (and after my death I have time:P) I'll exist again in the exact same state in the future, because the exact same series of object will be there somewhere. We simply look at the universe as a big random generator generating infinite amount of numbers and if it generates one specific number then that's a person. This also means that the probabiliy of you being 'resurrected' without that deadly disease (which killed you in the past) is not zero. Uhm, that's it, if you are patient you'll live forever:)
By the way there are a number of exciting side effects of this theory. This randomization is also valid of the world around you. You can be resurrected in an infinite number of different worlds, with an infinite number of special abilities, you can be rich, you can fly or anything which is physically possible:) In fact you can experience every possible thing in the world in infinite time.
The other side effect is that the past is infinite as well and probably you have done everything in the past.

Sorry if my english is confusing at times:)
Even though I agree that the Universe is infinite. I do not believe that you can reincarnate in the "exact" same way. If it were "exact", it would be the perceived verse you are entangled within at this moment. Some food for thought though, two seconds from now you will be in a completely different verse. When you wake up in the morning, if you wake up :/, I hope you do, you will be in another verse as well.